The bottom-up hard-wall model [1]}, [2]} defines confinement as the quantum mechanical square box: when we confine free solutions by putting a barrier, there appear eigenstates. In the particular case of the hardwall, the barrier is given by a D-brane transversal to the spacetime directions. This barrier is located at some \(z_c=1/\Lambda _N\) , with \(\Lambda _N\)  being an energy scale. Thus, we fix the dilaton field to be zero \(\Phi (\zeta )=0\) . Then, the solutions for the holographic potential are given by the free \(p\) -form in AdS, given above:
\(\phi _0^Z\left(\zeta \right)&=&\frac{\sqrt{2}\,\Lambda _N }{\left|J_{\Delta -1}\left(\alpha _{\Delta -2,1}\right)\right|}\,\zeta ^{\frac{1}{2}}\,J_{\Delta -2}\left[M_0(\Delta )\,\zeta \right]\\ M_0(\Delta )&=&\Lambda _N\,\alpha _{\Delta -2,1}\\\Lambda _N&=&\frac{M_{^4_2\text{He}}}{\alpha _{2,1}},\) 
